Final answer:
In the context of polar coordinates, equivalent points can be found by adding or subtracting multiples of 2π to the angle component or by considering the sign of the radius. For example, (4, -π/3) is equivalent to (4, -5π/3), and (-4, -π/3) is equivalent to (-4, 5π/3).
Step-by-step explanation:
To find equivalent polar points, we consider that adding or subtracting multiples of 2π radians to the angle component does not change its location. Also, a negative radius means the point is in the opposite direction of where it would be with a positive radius.
The original polar point we are comparing to is not given in the question, but assuming we are looking for points equivalent to any one point in the list, we would look for the angle differences of multiples of 2π radians and the sign of the radius.
Considering these rules, (4, -π/3) and (4, -5π/3) are equivalent since -5π/3 is the same angle as -π/3 plus 2*π. Similarly, (-4, -π/3) and (-4, 2π - π/3), which simplifies to (-4, 5π/3), are also equivalent, as well as (-4, -4π/3) and (4, 2π - 4π/3) or (4, -4π/3).